Introduction to Quantum Mechanics and Orbitals

Dec 5, 2024

Lecture Notes: Quantum Mechanics and Orbitals

Introduction to Orbitals

  • Orbital Definition: The most probable location to find an electron.
  • Bohr Model of the Atom: Circular orbits representing energy levels.

Energy Levels and Quantum Numbers

  • Principal Quantum Number (n)
    • Represents the energy level and size of the orbital.
    • As "n" increases, the distance from the nucleus increases.
    • Lower "n" values indicate electrons closer to the nucleus with lower energy.

Angular Momentum Quantum Number (L)

  • Describes the shape of the orbital
    • L = 0: s orbital (spherical shape)
    • L = 1: p orbital (dumbbell shape)
    • L = 2: d orbital (cloverleaf shape)
    • L = 3: f orbital (complex shape)
  • Sublevel Correspondence
    • L values determine sublevels: s, p, d, f

Relationship Between n and L

  • L ≤ n-1
    • n = 1: Only s sub-level (L=0)
    • n = 2: S and P sub-levels (L=0, 1)
    • n = 3: S, P, and D sub-levels (L=0, 1, 2)
    • n = 4: S, P, D, and F sub-levels (L=0, 1, 2, 3)

Magnetic Quantum Number (M<sub>L</sub>)

  • Describes the orientation of the orbital
    • For s sub-level: L=0, hence M<sub>L</sub>=0
    • For p sub-level: L=1, M<sub>L</sub> varies between -1 and 1
    • For d sub-level: L=2, M<sub>L</sub> varies between -2 and 2

Electron Spin Quantum Number (M<sub>S</sub>)

  • Electron Spin
    • Two possibilities: +1/2 (up spin) or -1/2 (down spin)
  • Pauli’s Exclusion Principle
    • Each electron in an atom has a unique set of four quantum numbers.

Examples

  • 2p<sub>5</sub> Electron Quantum Numbers

    • n = 2: Second energy level
    • L = 1: P sub-level
    • M<sub>L</sub> = 0: Orientation within P sub-level
    • M<sub>S</sub> = -1/2: Spin direction
  • 3d<sub>5</sub> Electron Quantum Numbers

    • n = 3: Third energy level
    • L = 2: D sub-level
    • M<sub>L</sub> = 2: Orientation within D sub-level
    • M<sub>S</sub> = +1/2: Spin direction

Conclusion

  • Engage with additional resources for further understanding.
  • Recommended further videos on quantum numbers and electron configurations.

For more examples and detailed explanations, visit the speaker's YouTube channel for a comprehensive chemistry playlist.